Answer to Question #248729 in Physics for James Andrew

Question #248729

A disoriented physics professor drives 3.25 km north, then 2.20 km west, and then 1.50 km south. Find the magnitude and direction of the resultant displacement using the component method.


1
Expert's answer
2021-10-10T15:57:26-0400

Let's first find xx- and yy-components of the resultant displacement:

dx=3.25 kmcos90+2.20 kmcos180+1.5 kmcos270=2.2 km,d_x=3.25\ km\cdot cos90^{\circ}+2.20\ km\cdot cos180^{\circ}+1.5\ km\cdot cos270^{\circ}=-2.2\ km,

dy=3.25 kmsin90+2.20 kmsin180+1.5 kmsin270=1.75 km.d_y=3.25\ km\cdot sin90^{\circ}+2.20\ km\cdot sin180^{\circ}+1.5\ km\cdot sin270^{\circ}=1.75\ km.

We can find the magnitude of the resultant displacement from the Pythagorean theorem:


d=dx2+dy2=(2.2 km)2+(1.75 km)2=2.81 km.d=\sqrt{d_x^2+d_y^2}=\sqrt{(-2.2\ km)^2+(1.75\ km)^2}=2.81\ km.


We can find the direction of the resultant displacement from the geometry:


θ=tan1(dydx),\theta=tan^{-1}({\dfrac{d_y}{d_x}}),θ=tan1(1.75 km2.2 km)=38.5 N of W.\theta=tan^{-1}({\dfrac{1.75\ km}{-2.2\ km}})=38.5^{\circ}\ N\ of\ W.

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